Developments of complex principal component analysis for an exploratory study of Pacific winds and El Niño Southern Oscillation

Multivariate analysis of complex data need appropriate exploratory procedures, able to deal with two-dimensional data. For this reason, complex principal component analysis has been enriched with an inner optimization, that fixes an intrinsic indeterminacy, allowing a better interpretation of the results and of their graphical representations. Considering that for complex variables two correlations—rotational and reflectional—make sense, widely linear components are introduced, based on a special real principal component analysis, able to deal with both correlations at the same time, also further optimizing the concentration of the explained inertia on the first components. In this paper, both methods are applied to the winds recorded in a small subset of TAO/TRITON array data during a time interval when both El Niño and La Niña phenomena occurred. Paralleled with the analysis of the corresponding sea surface temperatures, the factorial representations obtained through these methods show their different features while highlighting the winds variations due to these phenomena, this way contributing to a better understanding of the resulting climate variations.